It is shown that the extensive non-linearity which can be observed in the stress-strain response of CFRP submitted to tensile tests in angle-ply or off-axis configurations cannot be of viscoelastic nature. A simple model is proposed to evaluate the response of a lamina of glass- or carbon- reinforced plastic under tensile loading. This model is based on an exponential decrease of the shear and transverse moduli, with respect to the corresponding total strains. It has been experimentally assessed and successfully applied to fit the mechanical response of various [±θ] nS laminates under tensile testing. This model gives acceptable results up to the failure of those laminates which can be correlated with a quadratic criterion involving shear and normal stresses within the laminae. This model provides a framework to quantitatively study the effects of environmental conditions such as moisture or temperature on the mechanical response of these materials.